Self-consistent Polycrystal Model Research Articles

Coupling elasto-plastic self-consistent crystal plasticity and implicit finite elements: Applications to compression, cyclic tension-compression, and bending to large strains

In this work, we describe a finite element (FE) implementation of an elasto-plastic self-consistent (EPSC) polycrystal plasticity model termed FE-EPSC, which is intended for simulations of metal forming. To this end, we present an analytical Jacobian, which is necessary for the implicit coupling and ensuring a fast convergence. Every FE integration point is a material point that can be represented either by a single crystal or a polycrystalline material. The constituent crystal can deform by a combination of anisotropic elasticity, crystallographic slip, and deformation twinning. The model is validated and applied to a suite of tests, including monotonic compression, cyclic forward loading, unloading and reverse loading and non-monotonic four-point bending, and materials, such as different alloy compositions, crystal structures, and initial microstructures. The same FE-EPSC framework is applied for all these cases with the main differences pertaining to intrinsic properties, such as the available slip and twinning deformation modes, and the material parameters for activating and hardening of these modes. Full characterization for these parameters for high-purity α-Ti is presented here for the first time. Through these examples we show that, in addition to being predictive with great accuracy, the key advantage of this model lies in its versatility. It accounts for the development of backstress aided dislocation glide, thermally activated storage of dislocations, elastic anisotropy, crystallographic slip and deformation twinning via multiple modes, and de-twinning as well as multi-level homogenizations.

Examining the microtexture evolution in a hole-edge punched into 780 MPa grade hot-rolled steel

The deformation behavior in the hole-edge of 780MPa grade hot-rolled steel during the punching process was investigated via microstructure characterization and computational simulation. Microstructure characterization was conducted to observe the edges of punched holes through the thickness direction, and electron back-scattered diffraction (EBSD) was used to analyze the heterogeneity of the deformation. Finite element analysis (FEA) that could account for a ductile fracture criterion was conducted to simulate the deformation and fracture behaviors of 780MPa grade hot-rolled steel during the punching process. Calculation of rotation rate fields at the edges of the punched holes during the punching process revealed that metastable orientations in Euler space were confined to specific orientation groups. Rotation-rate fields effectively explained the stability of the initial texture components in the hole-edge region during the punching process. A visco-plastic self-consistent (VPSC) polycrystal model was used to calculate the microtexture evolution in the hole-edge region during the punching process. FEA revealed that the heterogeneous effective strain was closely related to the heterogeneity of the Kernel average misorientation (KAM) distribution in the hole-edge region. A simulation of the deformation microtexture evolution in the hole-edge region using a VPSC model was in good agreement with the experimental results.

Mechanical, microstructural behaviour and modelling of dual phase steels under complex deformation paths

This paper aims to identify the mechanisms associated to the transient hardening behaviour of dual phase steels under strain path changes, and to capture the observed material behaviours with appropriate constitutive models. First, three DP steel sheets with different amounts of martensite were tested under monotonic and various strain path changes. Second, microstructural analysis of the materials before and after strain path change were performed by means of SEM, TEM, and EBSD. The contribution of texture evolution on the mechanical behaviour was also assessed using the visco-plastic self-consistent (VPSC) polycrystal plasticity model. Transient hardening behaviour and permanent softening were observed in the tension–tension tests for all the studied DP steels. These behaviours were explained by the development of strain gradients during the first load resulting from strain accommodation incompatibilities between the ferrite and martensite phases. For the purpose of describing the macroscopic material behaviours, the enhanced homogeneous anisotropic hardening (HAH) model (Barlat et al., 2014) integrated with the Yld2000-2d anisotropic yield function were adopted for constitutive modelling. The simulation results were discussed in view of the microstructure evolution.

Dislocation structure in different texture components determined by neutron diffraction line profile analysis in a highly textured Zircaloy-2 rolled plate

A novel diffraction-based method has been developed to determine the substructure in terms of the fraction of prevailing slip systems and dislocation densities in multiple individual texture components of strongly textured materials. The method was applied to a strongly textured cold-rolled Zircaloy-2 sample, compressed along the normal direction of the rolled plate. Fourteen diffraction patterns were collected by time-of-flight neutron diffraction experiments at seven different purposely selected sample orientations. The diffraction peaks corresponding only to one single texture component out of the four prevailing components were identified and used to construct texture-specific diffraction patterns. The best five such patterns were evaluated by the convolutional multiple whole profile procedure of line profile analysis for the fractions of the prevailing 〈a〉-, 〈c + a〉- and 〈c〉-type slip systems and the corresponding dislocation densities. It is found that in the three texture components with thecaxis not parallel to the normal direction of rolling the average dislocation densities and fractions of slip-system types are the same. However, in the texture component with thecaxis parallel to the normal direction of rolling the fraction of the 〈a〉-type slip system is somewhat smaller than in the other components and that of the 〈c〉-type slip system is somewhat larger than zero. The fractions of the prevailing slip systems are in good correlation with literature data of self-consistent polycrystal plasticity modeling of Zircaloy-2.

A multiscale simulation framework of the accumulative roll bonding process accounting for texture evolution

The accumulative roll bonding process is one of the most prominent severe plastic deformation processes for obtaining sheet materials with ultra-fine-grained microstructures and high strength. The properties of such sheets differ significantly from those of conventionally rolled sheets. It is hence desirable to have a simulation framework that can accurately predict the material properties, including the evolving texture and anisotropy during processing. Here, we propose such a framework for multiple pass rolling using explicit finite elements and embedding the visco-plastic self-consistent (VPSC) polycrystal texture model for the material response. To facilitate multiple pass rolling, we propose a novel solution mapping scheme that transfers the material state from the deformed finite element mesh to a new one. Additionally, we implement a two-level parallelization scheme – with decomposition of the FE domain using message passing interface (MPI) and thread based parallelization of the material response using openMP – to ensure reduced simulation times. The predictive capabilities of the proposed framework are demonstrated by simulating the accumulative roll bonding of aluminum alloy AA5754 sheets. The simulations validate the working of the solution mapping scheme, and clearly show the development of a through thickness gradient of texture and anisotropy in the roll-bonded sheet after two passes.

Combined effects of anisotropy and tension–compression asymmetry on the torsional response of AZ31 Mg

In this paper it is demonstrated that only by accounting for the combined effects of anisotropy and tension–compression asymmetry at polycrystal level, it is possible to explain and accurately predict the room-temperature torsional response of a strongly textured AZ31 Mg material. This is shown by using two modeling frameworks, namely: a viscoplastic self-consistent (VPSC) polycrystal model, and a macroscopic plasticity model based on an yield criterion, developed by Cazacu et al. (2006), that accounts for both orthotropy and tension–compression asymmetry in plastic flow. It is shown that unlike Hill’s (1948) criterion, the latter macroscopic criterion quantitatively predicts the experimental results, namely: that the sample with axial direction along the rolling direction contracts, while the sample with axial direction along the normal direction elongates. Moreover, it is demonstrated that these experimentally observed axial strain effects can be quantitatively predicted with the VPSC polycrystal model, only if both slip and twinning are considered operational at single crystal level. On the other hand, if it is assumed that the plastic deformation is fully accommodated by crystallographic slip, the axial strains predicted by VPSC are very close with that predicted with Hill (1948) criterion, which largely underestimates the measured axial strain in the rolling direction, and predicts zero axial strain in the normal direction.

Mechanical responses and deformation mechanisms of an AZ31 Mg alloy sheet under dynamic and simple shear deformations

The mechanical responses and deformation mechanisms of AZ31 Mg alloy sheets were studied under dynamic (tension and compression) and simple shear deformations along different in-plane loading directions. This paper is a continuation of the author’s previous manuscript (Khan et al., 2011) on the quasi-static responses and texture evolution of AZ31 Mg alloy sheets. The strain-hardening rate (dσ/dε) of specimens under in-plane dynamic compression at room temperature showed a strong strain-rate dependency when deformation entered the dynamic region. The electron back-scattered diffraction (EBSD) technique was used to conduct texture analysis on each specimen after simple shear deformation under a quasi-static load (100s−1) at 150°C and after dynamic compression under a strain rate of 1500s−1 at RT and 150°C. Loading direction during simple shear deformation did not significantly affect either the texture evolution or the twinning evolution. Deformation temperature during dynamic compression affected both the texture evolution and the twinning evolution only slightly, but it significantly affected the kernel average misorientation (KAM) distribution in deformed grains. A visco-plastic self-consistent (VPSC) polycrystal model was successfully used to simulate the mechanical responses and the evolution of the initial texture in an AZ31 Mg alloy sheet during simple shear deformation and dynamic compression.

A constitutive model of twin nucleation, propagation and growth in magnesium crystals

A new constitutive model to describe twin nucleation, propagation and growth for magnesium crystals is developed and implemented in the recently developed Elastic Viscoplastic Self-Consistent polycrystal model. The new model explicitly takes into account the stress relaxation associated with twin nucleation. It is demonstrated that the new twinning model is able to capture key macroscopic features associated with twin nucleation, propagation and growth observed experimentally.

Effect of microstructural features on the planar anisotropy of the R-value in Cu-added bake-hardenable steels

Abstract This study was focused on investigating the effect that microstructural features have on the planar anisotropy of the plastic strain ratio ( R -value) in Cu-added bake-hardenable (BH) steel. Ti–Nb-added BH steel was used for a comparison of microstructural features and their effects on the planar anisotropy of an R -value. Quantitative and qualitative analyses of the precipitates for two hot-rolled BH steels were conducted via TEM. An EBSD technique was used to analyze the evolution of the microtexture in consecutive manufacturing processes of hot-rolling, cold-rolling and annealing. Microstructural features in cold-rolled specimens were explained in terms of the type of deformed grains. The stored energy distribution that developed in subgrains was used to explain the relatively high planar anisotropy of the R -value for Cu-added BH steel. A visco-plastic self-consistent (VPSC) polycrystal model was employed to calculate the planar anisotropy of the R -value for annealed BH steels.

Unexpected brass-type texture in rolling of ultrafine-grained copper

Performing large-strain rolling of initially ultrafine-grained copper obtained by eight passes in equal-channel angular pressing, a brass-type – rather than a copper-type – texture was achieved. Clearly, the deformation mechanism is different in ultrafine-grained materials for subsequent rolling. Using the viscoplastic self-consistent polycrystal model, we find that the deformation mechanism is associated with the activation of partial {1 1 1} 〈1 1 −2〉 slip and with a reduced quantity of geometrically necessary dislocations that lead to near Taylor polycrystal deformation conditions in ultrafine-grained copper.

Influence of deformation temperature on texture evolution in HPT deformed NiAl

NiAl is an intermetallic compound with a brittle-to-ductile transition temperature at about 300°C and ambient pressure. At standard conditions, it is very difficult to deform, but fracture stress and fracture strain are increased under high hydrostatic pressure. On account of this, deformation at low temperatures is only possible at high hydrostatic pressure, as for instance used in high pressure torsion. In order to study the influence of temperature on texture evolution, small discs of polycrystalline NiAl were deformed by high pressure torsion at temperatures ranging from room temperature to 500°C. At room temperature, a typical shear texture of body centred cubic metals is found, while at 500°C a strong oblique cube component dominates. These textures can be well simulated with the viscoplastic self-consistent polycrystal deformation model using the primary and secondary slip systems activated at low and high temperatures. The oblique cube component is a dynamic recrystallization component.

Investigation of deformation dynamics in a wrought magnesium alloy

In the present research, the real-time in-situ neutron diffraction measurements under a continuous-loading condition and elastic–viscoplastic self-consistent (EVPSC) polycrystal modeling were employed to study the deformation dynamics and the effect of the deformation history on plastic deformation in a wrought magnesium alloy. The experimental results reveal that pre-deformation delays the activation of the tensile twinning during the subsequent compression, mainly resulting from the residual strains. Detwinning does not occur until the applied stress exceeds the tensile yield strength during the reverse loading. It is believed that the grain rotation plays an important role in the elastic region during the reverse loading. The EVPSC model, which has been recently updated by implementing the twinning and detwinning model, was employed to characterize the deformation mechanism during the strain-path changes. The simulation result predicts well the experimental observation from the real-time in-situ neutron diffraction measurements. The present study provides a new insight of the nature of deformation mechanisms in a hexagonal close-packed (HCP) structured polycrystalline wrought magnesium alloy, which has significant implications for future work on studying the deformation mechanisms of HCP-structured materials.

A hierarchical multi-scale model for hexagonal materials taking into account texture evolution during forming simulation

Due to the absence of sufficient number of slip systems in hexagonal close packed (hcp) metals to accommodate arbitrary plastic deformation, mechanical twinning occupies an important role in the mechanical behavior of these metals. Twinning causes a significant and abrupt change in the orientation of crystals, whilst simultaneously affecting the hardening and plastic flow behavior of the material considerably. Modeling of forming processes of hexagonal close packed metals thus requires accounting for the evolution of texture and texture induced anisotropy, especially due to twinning. Additionally, the computational framework for the simulation of forming processes must be reliable and efficient in order to guarantee results in realistic time frames. In the present work, a phenomenological constitutive model consisting of an anisotropic yield function, associate flow rule and isotropic hardening, is coupled with the viscoplastic self-consistent polycrystal model in order to capture the slip and twinning activity, texture evolution and the evolving anisotropy during plastic deformation of hcp materials, similar to a hierarchical multi-scale modeling framework proposed by Van Houtte et al. [41] for cubic metals. To account for texture evolution during plastic deformation, the parameters involved in the anisotropic yield function are regularly updated based on mechanical test data obtained from the polycrystal model at the micro-scale. The parameter update is performed at discrete steps instead of every increment. The developed model is applied to describe the behaviors of pure zirconium at liquid nitrogen temperature. The results of the numerical simulations were found to be good agreement with experimental results, and at acceptable computation time.

Reprint of: Shear banding in sub-microcrystalline nickel at 4 K

A flat specimen of sub-microcrystalline nickel was tensile tested at 4K until fracture occurred and subsequently investigated by electron backscatter diffraction in a high resolution scanning electron microscope in order to deduce the local texture in the near crack area. Thus, two sets of intersecting fine slip markings observed on the surface (under ±55° with respect to the tensile axis) could be explained as a result of localized simple shear in the bulk material underneath the slip markings. The overall amount of shear in the region near the crack was estimated to be 1.25 based on texture simulations using the viscoplastic self-consistent polycrystal model.

Asymmetric Rolling of Interstitial-Free Steel Using Differential Roll Diameters. Part II: Microstructure and Annealing Effects

The effects of annealing on the microstructure, texture, tensile properties, and R value evolution of an IF steel sheet after room-temperature symmetric and asymmetric rolling were examined. Simulations were carried out to obtain R values from the experimental textures using the viscoplastic self-consistent polycrystal plasticity model. The investigation revealed the variations in the textures due to annealing and symmetric/asymmetric rolling and showed that the R values correlate strongly with the evolution of the texture. An optimum heat treatment for the balance of strength, ductility, and deep drawability was found to be at 873 K (600 °C) for 30 minutes.

Shear banding in sub-microcrystalline nickel at 4 K

A flat specimen of sub-microcrystalline nickel was tensile tested at 4K until fracture occurred and subsequently investigated by electron backscatter diffraction in a high resolution scanning electron microscope in order to deduce the local texture in the near crack area. Thus, two sets of intersecting fine slip markings observed on the surface (under ±55° with respect to the tensile axis) could be explained as a result of localized simple shear in the bulk material underneath the slip markings. The overall amount of shear in the region near the crack was estimated to be 1.25 based on texture simulations using the viscoplastic self-consistent polycrystal model.

Effect of the initial texture components of hot-rolled BH steel on the evolution of deformation texture and stored energy during the cold-rolling process

A visco-plastic self-consistent polycrystal model was used to investigate the effect of texture gradients through the thickness direction of hot-rolled bake-hardening steel on the evolution of deformation texture and stored energy during a cold-rolling process. The theoretical texture evolution was in good agreement with the experimental texture evolution, as measured using the electron back-scattering diffraction technique. The VPSC polycrystal model was also used to explain the individual contribution of major texture components to the evolution of deformation texture and stored energy during cold-rolling. The results demonstated that the biased bimodal distribution of stored energy in major texture components contributed to a distinct bimodal distribution of stored energy at the center and surface regions of cold-rolled BH steel.

Thermal residual strains in depleted α-U

Lattice strains induced by cooling textured, depleted U, from 500 °C to ambient temperature are measured using in situ neutron diffraction and simulated using an elastoplastic self-consistent polycrystal model. The results show that the high anisotropy of the single-crystal thermoelastic response induces thermal stresses sufficient to cause plastic relaxation. Incorporation of ½ 〈 1 1 ¯ 0 〉 { 1 1 0 } slip enables modeling of the observed internal strain evolution, although diffusional effects may also contribute to the observed relaxation.

Experimental and numerical investigations of yield surface, texture, and deformation mechanisms in AA5754 over low to high temperatures and strain rates

The effects of strain rate and temperature on the yield and flow stress of AA5754 sheets are presented under uniaxial (tension and compression), dynamic (tension), and simple shear loading conditions. The present study investigates the anisotropic behavior of AA5754 sheets through experiments performed in the rolling (RD), 45° to rolling (DD), and transverse to rolling (TD) directions at room and elevated temperatures. The experimental results show that the strain rate sensitivity varied from negative at room temperature to positive at elevated temperatures (>150°C), and the anisotropy was inversely proportional to the strain rate. Texture analysis was conducted on the specimens after uniaxial tension and simple shear deformation, using the neutron diffraction and electron back-scattered diffraction (EBSD) techniques. Rotation rate maps and orientation stability parameters, determined by the rate-sensitive model, were used to explain the kinematic stability of the initial texture components in AA5754 sheets during uniaxial tension and simple shear deformation. A visco-plastic self-consistent (VPSC) polycrystal model was used to simulate the evolution of the initial texture components in AA5754 sheets during uniaxial tension and simple shear deformation.

A constitutive model of twinning and detwinning for hexagonal close packed polycrystals

A new constitutive model to describe twinning and detwinning for polycrystalline materials with the hexagonal close packed (HCP) crystallographic structure is developed and implemented in the recently developed elastic viscoplastic self-consistent (EVPSC) polycrystal model. The new model is then applied to magnesium alloy Mg–3 Al–1 Zn (AZ31B) sheet under cyclic loadings and strain path changes. It is demonstrated that the new twinning model is able to capture key features associated with twinning and detwinning observed experimentally.